Download The dual nature of public goods and congestion: the role of fiscal

The dual nature of public goods and
congestion: the role of fiscal policy revisited
Santanu Chatterjee
Sugata Ghosh
Department of Economics, University of
Georgia
Department of Economics and Finance, Brunel
University
Abstract. The role of fiscal policy is examined when public goods provide both productive
and utility services. In the presence of congestion, the consumption tax is shown to
be distortionary. Optimal fiscal policy involves using consumption-based instruments
in conjunction with the income tax. An income tax-financed increase in government
spending dominates both lump-sum and consumption tax-financing. Replacing the lumpsum tax with an income tax to finance a given level of spending dominates introducing an
equivalent consumption tax. These results contrast sharply with the literature, where the
consumption tax is generally viewed as the least distortionary source of public finance.
JEL classification: E21, E62, H21, H41, H54
La nature duale des biens publics et de la congestion : un ré-examen de la politique fiscale.
On ré-examine le rôle de la politique fiscale quand les biens publics fournissent à la fois
des services productifs et de bien-être. Quand il y a congestion, on montre que la taxe
sur la consommation crée des distorsions. La politique fiscale optimale consiste à faire
bon usage des taxes sur la consommation en conjonction avec l’impôt sur le revenu.
Une dépense gouvernementale financée par l’impôt sur le revenu est préférable à un
financement par un paiement forfaitaire ou une taxe sur la consommation. Remplacer
le paiement forfaitaire par un impôt sur le revenu pour financer un niveau donné de
dépense vaut mieux qu’introduire une taxe équivalente sur la consommation. Ces résultats
contrastent vivement avec ce qu’on trouve dans la littérature spécialisée, où l’on considère
généralement la taxe sur la consommation comme la source de finance publique qui crée
le moins de distorsion.
We would like to thank Stephen Turnovsky and an anonymous referee for valuable comments
that have substantially improved the paper. The paper has also benefited from presentations at
the Royal Economic Society Annual Conference in Warwick, the Centre for Growth and
Business Cycle Research Conference in Manchester, and the Third Annual Conference on
Economic Growth and Development at the Indian Statistical Institute, New Delhi. This paper
was previously circulated under the title ‘Public goods, congestion, and fiscal policy: do
consumption-based instruments matter?’ The usual disclaimer applies. Email: [email protected];
Sugata.Ghosh@ brunel.ac.uk
Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 44, No. 4
November / novembre 2011. Printed in Canada / Imprimé au Canada
0008-4085 / 11 / 1471–1496 / Canadian Economics Association
C
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S. Chatterjee and S. Ghosh
1. Introduction
Objectives and motivation. Public goods and associated externalities provide a
crucial channel through which government spending and taxation policies affect private resource allocation and social welfare. In analyzing the link between public goods and macroeconomic performance, most of the literature has
compartmentalized public goods into two distinct types: (i) those that impinge
directly on productivity, thereby entering the production process as a public input complementary to private capital and labour, and (ii) those that are purely
welfare-enhancing, thereby interacting with private consumption in the utility
function.1 In this paper, we argue that most public goods, such as infrastructure,
education, healthcare services, and law and order, play a dual role in influencing
private economic activity by simultaneously affecting both private productivity
and utility (welfare). Consequently, the dichotomy in defining public goods can
lead to inaccurate implications for the design and evaluation of fiscal policies.
By departing from this standard assumption of dichotomy, we derive a set of
new results linking fiscal policy to an economy’s structural characteristics and its
macroeconomic performance, and thereby synthesize two seemingly independent
strands of literature on this issue.
The following examples might help set this discussion in perspective. Consider economic infrastructure, which is, without exception, treated purely as a
productivity-enhancing input in the production process. Roads and highways,
apart from influencing productivity by facilitating the transportation of goods
and services, might also be an important source of utility to consumers, who
might get pleasure out of driving or taking road trips.2 Similar examples can
be offered for other aspects of infrastructure as well, such as power and water
supply, transport and communication, and so on. Education is another example
of a public good whose dual role is often overlooked. Its productivity-enhancing
role is underlined by the economy’s set of skills, knowledge base, human capital,
and, ultimately, a more productive workforce. It can also be argued that altruistic
parents derive satisfaction from sending their children to good schools, with the
1 One strand of literature, starting with Bailey (1971) and with later contributions by Aschauer
(1988) and Barro (1989), highlights the welfare-enhancing properties of public goods by
focusing on the substitutability between public and private consumption in the utility function.
On the other hand, Gramlich (1994) reviews the empirical evidence that suggests that
government investment expenditures may have large productivity effects on the economy. A
second strand of research therefore focuses on the productivity-enhancing role of public
investment goods, such as infrastructure; see Arrow and Kurz (1970) for an early analysis, and
Barro (1990), Futagami, Morita, and Shibata (1993), Baxter and King (1993), and Glomm and
Ravikumar (1994) for later contributions. Though Turnovsky and Fisher (1995) and Turnovsky
(2004) study both public consumption and investment, they are modelled as individually distinct
goods. Another recent contribution, by Economides, Park, and Philippopoulos (2011), also
distinguishes between productivity and utility-enhancing public goods in analyzing second-best
optimal policy in a Ramsey model.
2 The New York Times reported that about 87% of all vacation travellers in the U.S. (38 million
people) used the country’s interstate highway system for road trips during the 2006 Memorial
Day weekend.
Dual nature of public goods and congestion
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intention of enabling them to be better citizens in the future. Moreover, in developing countries that lack credit markets, investment in a child’s education is often
seen as a means of providing social insurance for parents in their old age. Further,
in many countries (and certainly in the US), school facilities are regularly used
for recreational activities such as fairs and sporting events, which provide direct
utility benefits to users. This argument holds for traditionally defined public consumption goods as well, such as law and order, national parks, defence. While
these goods might directly affect the utility consumers derive from them, they
can also have significant productivity benefits (by providing security, protecting
property rights, or reducing stress).3 In essence, most public goods should be
viewed as providing a composite bundle of services, rather than targeting some
specific aspect of economic activity (such as production or consumption).
The objective of this paper is to study the design and impact of fiscal policy
on growth and welfare when (i) the aggregate stock of a composite public good
simultaneously provides both consumption and productive services, and (ii) these
services are subject to differential degrees of relative congestion. Therefore, agents
in the economy (e.g., consumers and firms) can derive different types of services
(e.g., utility and productivity) from the accumulated stock of the same public
good. Further, the degree of rivalry (i.e., congestion) generated may also vary
across agents, depending on the underlying usage of the public good. For example,
power outages and shortages in water supply during peak ‘usage’ seasons such
as summer are common examples of congestion in many developing countries
(World Bank 1994). However, the disutility caused by a power outage for a
household may be quite different from the loss in productivity suffered by a
firm or worker. Similar examples can be motivated for highway or air-traffic
congestion as well. This aspect of the paper clearly distinguishes itself from
the existing literature, where the effects of congestion are restricted to either
production or utility, depending on the type of public good (i.e., consumption or
investment) being modelled.4
Value-added. Our contributions are threefold. First, we highlight a new mechanism through which a consumption tax might impact growth and welfare.5 In
3 Tanzi and Schuknecht (1997, 2000) find that government provision of education, health, public
pensions, and social insurance has led to increases in the literacy and life-expectancy rates and
reductions in infant mortality rates and unemployment insecurity in the OECD countries over
the 1913–1990 period, during which there was a fourfold increase in public spending as a
proportion of GDP. In effect, they make the argument that traditionally defined public ‘capital’
goods contribute as much to social welfare as do public ‘consumption’ goods.
4 Congestion is often used as a classic example of rivalry associated with public goods, and its
effects on growth, welfare, and the design of optimal fiscal policy have been studied by several
authors, including Edwards (1990), Barro and Sala-i-Martin (1992), Fisher and Turnovsky
(1998), and Eicher and Turnovsky (2000).
5 The consumption tax has a long history in economics, dating back to Hobbes (1651), with
Fisher (1937) and Kaldor (1955) providing the early contributions in the 20th century; see
Atkinson and Stiglitz (1980) for a review of the early literature and Gentry and Hubbard (1997)
for a discussion on the distributional effects of consumption taxes. More recently, the
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the context of endogenous growth, the only condition under which a consumption tax is distortionary is when the labour-leisure choice is endogenous (see, e.g.,
Milesi-Ferretti and Roubini 1998 and Turnovsky 2000 for some recent examples).
In contrast, we show that when public goods provide ‘dual’ services and the utility services are subject to congestion, a consumption tax is indeed distortionary,
affecting both the economy’s dynamic adjustment and its equilibrium resource
allocation, even when the labour supply is exogenous. The dual nature of the
public good plays an important role in this result by linking the marginal utility
of consumption and its relative price to the marginal return on private capital.6
Second, the above feature enables us to generalize some important results on
optimal fiscal policy in the context of public goods and growth. Most of the
existing literature relies on the income tax as the sole corrective fiscal instrument
for congestion, with the consumption tax playing the role of a non-distortionary
lump-sum tax, used to balance the government’s budget (see Barro and Sala-iMartin 1992; Turnovsky 1996). However, our analysis assigns an important role
to consumption-based fiscal instruments as a complement to the income tax in
correcting for different sources of congestion. This is due to the distortionary
role played by the consumption tax (or subsidy) in our set-up. This refinement
is possible only when one acknowledges the dual nature of a public good and
the differential congestion externalities its usage generates. More important, we
demonstrate that most of the standard results in the literature on optimal fiscal
policy and congestion can be conveniently derived as special cases of our more
general model.
Third, given that both income and consumption taxes are distortionary in
our set-up, we conduct several policy experiments to compare numerically their
relative efficacy as financing tools for government spending. For empirically plausible values of the elasticity of substitution in production, financing an increase
in government spending through an increase in the income tax rate dominates
lump-sum and consumption tax financing, when the services from the public
good are congested. In the presence of congestion, replacing the lump-sum tax
with an income tax to finance a given level of government spending improves
consumption tax has also occupied a significant place in the political debate on tax reform in the
United States. See, for example, the 2003 United States Economic Report of the President (chap.
5, 175–212) for a discussion on the pros and cons of a consumption-based tax system relative to
an income-based system.
6 The possibility of a dual role played by public investment was first suggested by Arrow and Kurz
(1970, chap. 1), though a formal treatment was not provided. In a recent contribution, Agenor
(2008) develops a model where, within a Cobb-Douglas production setting, infrastructure
services influence the production of goods and the provision of healthcare services. The latter, in
turn, affects both individual welfare and productivity. The focus of this paper, however, is very
different. While Agenor (2008) focuses on the expenditure side of the government’s budget and
the potential trade-offs between spending on infrastructure and healthcare, we focus on the
revenue side and the differential effects of congestion: using a more general CES production
structure, we characterize the appropriate mix of income and consumption-based tax
instruments that can be used to correct for the different types of congestion generated by a
composite public good.
Dual nature of public goods and congestion
1475
welfare by reducing congestion. In contrast, the introduction of an equivalent
consumption tax actually worsens welfare by increasing congestion. These results
also contrast sharply with the existing literature, where the consumption tax is
often viewed as the least distortionary source of financing government spending.
The rest of the paper is organized as follows. Section 2 develops the analytical framework using a composite public good. Section 3 characterizes resource
allocation in a centrally planned economy, which yields the benchmark first-best
optimum. Section 4 derives the macroeconomic equilibrium in a decentralized
economy and discusses the design of optimal fiscal policy. In section 5, we conduct
a numerical analysis of the model and its dynamic properties, with a particular
emphasis on welfare. Section 6 concludes the paper.
2. Analytical framework
We consider a closed economy populated by N infinitely lived identical agents,
each of whom maximizes intertemporal utility from the consumption from a
private good C, and the services derived from the accumulated economy-wide
stock of a composite public good, Kg :
U ≡ U(C, Kg ) =
0
∞
⎤
⎡ 1−σc θ γ
K
1⎣
⎦ e−βt dt,
C Kg
γ
K̄
(1)
− ∞ < γ ≤ 1, 0 ≤ θ ≤ 1, 0 ≤ σc ≤ 1,
where θ denotes the relative importance of the public good in the utility function.
The available stock of the public good is non-excludable, but the services derived
from it by an individual agent may be subject to rivalry, in the form of relative
congestion. In other words, the ‘utility’ benefits derived by the agent from the
composite public good depend on the usage of its own private capital (K), relative
to the aggregate economy-wide usage (K̄).7 σ c parameterizes the degree of relative
congestion associated with the (utility) benefits derived from the public good.
The public good, apart from generating utility benefits for the representative
agent, is also available for productive purposes. Each agent produces a private
good, whose output is given by Y , using a CES technology, and its individual
stock of private capital and the economy-wide stock of the public good serve as
factors of production. However, the productive services derived from the public
7 The use of private capital to characterize congestion from the public good can be motivated by a
simple example: suppose that private vehicles are used to transport goods or labour during the
week, but for leisure activities during the weekend.
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good may also be subject to congestion, in a manner similar to (1):
Y = A αK −ρ + (1 − α) Kg
K
K̄
1−σy −ρ − ρ1
,
(2)
0 < α < 1, − 1 < ρ < ∞, 0 ≤ σy ≤ 1,
where σ y measures the degree of relative congestion associated with the productive benefits derived from the composite public good.8 The elasticity of
substitution between private capital and the public good is given by s =
1/(1 + ρ).9
The parameterization of θ in (1) provides a convenient tool by which the role
of the public good in influencing economic activity can be defined. For example,
when θ > 0, the public good plays a dual role in the economy, by providing both
productive and utility services. On the other hand, when θ = 0, the public good
is just a productive input with no direct utility benefits. This case corresponds to
the standard public capital-growth model found in the literature, as in Futagami,
Morita, and Shibata (1993).
The accumulation of public capital is enabled by the flow of new public
investment, given by
K̇g = G − δg Kg ,
(3)
where G represents the flow of expenditures on the public good, which may
be undertaken by either a social planner or a government, and δ g is the rate
of depreciation of the stock of public capital. Finally, the economy’s aggregate
resource constraint is given by
K̇ = Y − C − G − δK K,
(4)
where δ K denotes the depreciation rate for private capital.
The analytical description of the model will proceed sequentially in the following manner. First, we will describe the allocation problem in a centrally planned
economy. Given this ‘first-best’ benchmark equilibrium, we will then derive the
equilibrium in a decentralized economy. This sequential analysis will enable us to
8 In our specification, when σ i = 1(i = c, y), there is no congestion associated with the public
good. In that case, the public good is a non-rival good available equally to all agents. On the
other hand, σ i = 0 represents a situation of proportional congestion, where congestion grows
with the size of the economy. The case where 0 < σ i < 1 represents partial congestion. It is also
plausible that the degrees of relative congestion in the utility and production functions are
distinct, that is, σ c = σ y .
9 Assuming flexibility in the production structure by adopting a CES technology is useful for
analyzing the efficacy of fiscal policy shocks as the degree of factor substitutability changes.
When s = 1(ρ = 0), we obtain the familiar Cobb-Douglas specification. On the other hand, as
s → 0(ρ → ∞), (3) converges to the fixed-proportions production function, and when s → ∞
(ρ → −1), there is perfect substitutability between private capital and the public good.
Dual nature of public goods and congestion
1477
characterize the design of optimal fiscal policy in the decentralized economy. The
crucial behavioural difference between the centrally planned economy and the
decentralized one lies in the way the congestion externalities are internalized. In
the centralized economy, the social planner recognizes the relationship between
the stocks of individual and aggregate private capital, K̄ = NK, ex ante. However, in the decentralized economy, the representative agent fails to internalize
this relationship, although it holds ex post, in equilibrium. As a result, the resource allocation problem in the decentralized economy is subject to the various
sources of congestion described in (1) and (2), and consequently is suboptimal.
Optimal fiscal policy in the decentralized economy would then entail deriving
the appropriate tax and expenditure rates for the government that would enable
a replication of the equilibrium in a centrally planned economy.
3. A centrally planned economy: the first-best equilibrium
Since the planner internalizes the effects of congestion ex ante, we set K̄ = NK
and normalize N = 1. The planner’s utility and production functions then take
the form
∞
U=
0
γ
1
CKgθ e−βt dt
γ
− 1
Y = A αK −ρ + (1 − α)Kg−ρ ρ .
(1a)
(2a)
It is also convenient to begin with the assumption that the planner allocates
a fixed fraction, g, of output to investment in the public good, to sustain an
equilibrium characterized by endogenous growth. We will relax this assumption
in section 3.2 to characterize optimal public investment.
K̇g = G − δg Kg = gY − δg Kg , 0 < g < 1.
(5)
The planner chooses consumption and the accumulation of private capital
and the public good by maximizing (1a) subject to (4) and (5), while taking note
of (2a) and (3). The equilibrium relationships will be described in terms of the
following stationary variables: z = Kg /K, the ratio of the stock of the public good
to private capital, c = C/K, the ratio of private consumption to private capital,
and y = Y /K, the output-private capital ratio. Under the assumption that g is
arbitrarily fixed, the optimality conditions are given by
C γ −1 Kgθγ = λ
(6a)
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S. Chatterjee and S. Ghosh
αA−ρ [(1 − g) + qg] y1+ρ − δK = β −
λ̇
λ
y 1+ρ θ c λ̇
q̇ 1
+ (1 − α)A−ρ [(1 − g) + qg]
− δg = β − ,
+
q q
z
q z
λ
(6b)
(6c)
where λ is the shadow price of private capital, q is the shadow price of the public
good relative to that of private capital, and y = A[α + (1 − α)z−ρ ]−1/ρ .
The optimality conditions (6a)–(6c) can be interpreted as follows. The
marginal utility of consumption equals the shadow price of private capital in
(6a), while (6b) equates the rate of return on private investment to the corresponding return on consumption. An analogous interpretation holds for (6c),
which equates the return on public investment to that on consumption. The first
term on the left-hand side of (6c) describes the capital gains emanating from
the rate of change in its real price q (given that private capital is treated as the
numeraire good). Since the public good plays a dual role in this economy, both
as a consumption and an investment good, its social return is derived from two
sources: (i) the return from production, given by the second term on the left-hand
side of (6c), and (ii) the return from utility, given by the term θ (c/z), which measures the marginal rate of substitution between the private consumption good
and the stock of the public good.
3.1. Macroeconomic equilibrium
Given the presence of two capital stocks, the equilibrium will be characterized by
transitional dynamics around the steady state. The core dynamics of the centrally
planned economy can be expressed by the evolution of the stationary variables
z, c, and q, derived from (4), (5), and (6):
− 1
1
ż
= gA [(1 − α) + αzρ ]− ρ − δg − A(1 − g) α + (1 − α)z−ρ ρ + c + δK (7a)
z
αA−ρ [(1 − g) + qg]y1+ρ + θ γ g(y/z) − δg − (β + δK )
ċ
=
c
1−γ
− A(1 − g)[α + (1 −
1
α)z−ρ ]− ρ
(7b)
+ c + δK
c
z −(1+ρ) 1+ρ
+ q(δg − δK ). (7c)
y
−θ
q̇ = qA−ρ [(1 − g) + qg] α − (1 − α)
q
z
The steady-state equilibrium is attained when ż = ċ = q̇ = 0 and is characterized by balanced growth and a constant relative price of the public good.
Denoting the steady-state levels by z̃, c̃, and q̃, and given a predetermined policy
Dual nature of public goods and congestion
1479
g, the behaviour of the dynamic system (7) can be expressed in a linearized form
around the steady-state equilibrium:
(8)
Ẋ = X − X̃ ,
where X = (z, c, q), X̃ = (z̃, c̃, q̃), and represents the 3 × 3 coefficient matrix
of the linearized system.10
3.2. Optimal public expenditure
Instead of allocating an arbitrarily fixed fraction of output to expenditure on
the public good, the planner can plausibly make an optimal choice with respect
to the public spending rate g. Let the optimal share of public expenditure in
output be ĝ, which is to be derived endogenously from equilibrium. Performing
this optimization, we find that
q̂ = 1.
(9)
In other words, in choosing the optimal quantity of public expenditure, the
planner must ensure that the shadow prices of private capital and the public
good are equalized along the transition path. Substituting (9) into the steadystate conditions corresponding to (7), we can write the steady-state conditions
for the planner as follows (‘∧ ’ denotes the steady-state value of a variable when g
is set optimally):11
− 1
1
ĝA [(1 − α) + αẑρ ]− ρ = A(1 − ĝ) α + (1 − α)ẑ−ρ ρ − ĉ
(10a)
− 1
αA−ρ ŷ1+ρ + θ γ ĝ (ŷ/ẑ) − β
= A(1 − ĝ) α + (1 − α)ẑ−ρ ρ − ĉ
1−γ
(10b)
A
−ρ
ĉ
−(1+ρ)
1+ρ
.
α − (1 − α)ẑ
ŷ
=θ
ẑ
(10c)
Given (9), we can solve (10a)–(10c) for the optimal steady-state values of ẑ, ĉ,
and ĝ.
An interesting point to note here is that (9) implies q̇ = 0 at all points of time.
Therefore, the core dynamics are independent of the (unitary) real shadow price
of the public good. Substituting (9) into (7b) and noting (7a), we can easily verify
that when g is set at its socially optimal level, the dynamics are reduced to a
10 Details regarding the linearized dynamics are available upon request. We have numerically
verified that the linearized dynamic system (8) is characterized by one stable (negative) and two
unstable (positive) eigenvalues, which generates saddle-point behaviour.
11 We set δ K = δ g = 0 in this section, without any loss of generality.
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second-order system and can be expressed solely in terms of z and c.12 When the
planner optimally allocates output to investment in the public good, the resource
costs appearing in (6b) and (6c) are no longer relevant. However, in evaluating
the marginal costs and benefits of the private and public expenditure decisions,
the planner must consider the fact that allocating an extra unit of output to the
public good provides not only a productivity return, but also a utility return. This
aspect of the model represents a significant departure from earlier work regarding
the optimality of public investment in endogenous growth models. For example,
Turnovsky (1997) finds that when g is chosen optimally, the economy is always
on a balanced growth path and devoid of transitional dynamics. However, in this
more generalized set-up, once the social planner chooses the optimal allocation
of g, the stationary variables z and c are not constant, but evolve gradually along
the transition path, while the social planner ensures that the shadow prices of
private capital and the public good are always equalized. The key point here
is that since the social return from the public good is derived from both utility
and production, the corresponding investment in private capital must track this
return along the transition path for (9) to hold. As a result, z and c must adjust
accordingly at each point in time, until the steady-state equilibrium is attained.
It is easy to demonstrate that the relative importance of the public good in
the utility function (θ ) plays a crucial role in this result. To see this, assume
that θ = 0 in (10). Given that q̂ = 1, it is immediately evident from (10c) that
1
ẑ = [(1 − α)/α] 1+ρ . This implies that ż = 0 at all points of time. Consequently,
from (10b), it turns out that ċ = 0 must hold if the transversality conditions are to
be satisfied. Therefore, in the special case where θ = 0, the economy is always on
its balanced growth path and there is no dynamic adjustment. This is essentially
the result obtained in Turnovsky (1997). On the other hand, once the dual nature
of the public good is internalized, that is, θ > 0, the equilibrium is characterized
by a transitional adjustment path. We can then conclude that the utility function
(1) represents a general specification, from which earlier results in the literature
can be derived as special cases, depending on the magnitude of θ .
4. A decentralized economy
We now consider the case of a decentralized economy where the government plays
a passive role, while the representative agent makes its own resource allocation
decisions. There are two differences between this regime and the centrally planned
economy described in section 3. First, the government now provides the entire
stock of the public good using the financial and policy instruments at its disposal,
while the representative agent takes this stock as exogenously given in making its
private allocation decisions. Second, the representative agent does not internalize
¯ X − X̃ , where
12 In this case, the core dynamics reduce to a second-order system given by Ẋ = ¯ represents the 2 × 2 coefficient matrix of the linearized system.
X = (z, c), X̃ = (z̃, c̃), and Dual nature of public goods and congestion
1481
the effects of the two sources of congestion externality, σ c and σ y . The utility
function for the representative agent in this regime is therefore given by (1), while
the production function is given by (2). The agent accumulates wealth in the form
of private capital and holdings of government bonds, subject to the constraint
K̇ + Ḃ = (1 − τy )(Y + rB) − (1 + τc )C − T − δK K,
(11)
where r is the interest earnings on government bonds, τ y is the income tax rate,
τ c is the consumption tax rate, and T is a lump-sum tax. Taking the stock
of Kg as given, the agent chooses its flow of consumption, private investment,
and holdings of government bonds to maximize (1), subject to the flow budget
constraint (11) and the accumulation rule for private capital in (3), while taking
note of (2). It is important to note here that in performing its optimization, the
representative agent fails to internalize the relationship K̄ = NK, although it will
hold ex post in equilibrium. As before, we will express the equilibrium in terms of
the stationary variables z and c, and normalize N = 1, without loss of generality.
Since the agent does not make an allocation decision with respect to the public
good, its shadow price, q, is not relevant. The optimality conditions for the agent
are
C γ −1 Kgθγ = λ(1 + τc )
(12a)
λ̇
λ
(12b)
(1 − τy )A−ρ [α + (1 − α)(1 − σy )z−ρ ]y1+ρ + θ (1 − σc )(1 + τc )c − δK = β −
β−
λ̇
= (1 − τy )r.
λ
(12c)
The interpretation of the optimality conditions (12a)–(12b) is analogous to
that of the centrally planned economy, except that in (12b), the rate of return on
private capital is subject to the sources of congestion in production and utility.
The presence of congestion raises the total market return on private capital when
K increases, by increasing the productive and utility services derived from the
stock of the public good. The last term on the left-hand side of (12b), θ (1 − σ c )
(1 + τ c )c, represents the marginal rate of substitution between consumption and
private capital generated by congestion in the utility function. In other words,
it reflects the price of consumption relative to private capital. This is the crucial
channel through which a consumption tax affects the agent’s resource allocation
decisions along the equilibrium path. Equation (12c) equates the rate of return on
consumption to the return on government bond holdings and represents the noarbitrage condition that equalizes the returns from consumption, private capital,
and government bonds.
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The government provides the necessary expenditure for the provision of the
public good, which accumulates according to (5), and g now represents the
(exogenous) fraction of output allocated by the government to the accumulation
of the public good. Public investment is financed by tax revenues and issuing
government debt:
Ḃ = r(1 − τy )B + G − τy Y + τc C + T .
(13)
Combining (13) with (11) yields the aggregate resource constraint for the economy, given by (4). The steady-state equilibrium in the decentralized economy is
given by
− 1
1
gA [(1 − α) + αz̃ρ ]− ρ − δg = A(1 − g) α + (1 − α)z̃−ρ ρ − c̃ − δK
(14a)
(1 − τy )A−ρ α + (1 − α)(1 − σy )z̃−ρ ỹ1+ρ + θ (1 − σc )(1 + τc )c̃ + γ g (ỹ/z̃) − δg − (β + δK )
1−γ
− 1
= A(1 − g) α + (1 − α)z̃−ρ ρ − c̃ − δK .
(14b)
Equations (14a) and (14b) can be solved for the steady-state values of z̃ and
c̃. The dynamic evolution of the economy and the steady-state equilibrium are
independent of the shadow price of the public good, q. This happens because the
representative agent treats the government-provided stock of the public good as
exogenous to its private decisions. As a result, the agent does not internalize the
effect of its private investment decisions on the evolution of the public good.
4.1. Income versus consumption taxes in the presence of congestion
The macroeconomic equilibrium for the decentralized economy in (14) provides
some new insights on the interaction between private resource allocation decisions and the government’s fiscal instruments. Interestingly, the consumption tax,
τ c , can be distortionary in this set-up, affecting both the dynamic evolution and
the steady-state equilibrium of the economy. This is a significant result, since our
framework does not assume an endogenous labour-leisure choice which, in the
literature, has been a crucial channel for a consumption tax to be distortionary.
However, two conditions must be simultaneously satisfied for the consumption
tax to have distortionary effects in our framework: (i) the public good plays a
dual role by providing both utility and productive services (θ > 0), and (ii) the
utility services derived from the public good are subject to congestion (0 < σ c <
1). As discussed in the introduction, both these conditions are plausible in the
context of most public goods. Intuitively, a change in the consumption tax rate
will increase the marginal rate of substitution between private consumption and
private capital through the utility services derived from the public good, which in
turn affects the market return from private capital, given by (12b). Therefore, the
Dual nature of public goods and congestion
1483
dual nature of the composite public good and congestion generated by its utility
services provide an alternative transmission mechanism for the consumption tax
in affecting private economic decisions.
The steady-state equilibrium in (14a) and (14b) also throws some light on the
way an income and a consumption tax might impact the economy in the presence
of congestion externalities. Since both the utility and productive services from the
public good are congested by private usage, the market return on private capital
in a decentralized economy is above its socially optimal level, given by (6b).
Therefore, the decentralized equilibrium is characterized by ‘too much’ private
investment and ‘too little’ private consumption, relative to the social optimum.
In this scenario, the goal of public policy would be to reduce the market return
on private capital. From (12b) and (14), it is clear that an increase in income tax
will help alleviate congestion by reducing the after-tax marginal return on private
capital. On the other hand, an increase in the consumption tax works exactly in
the opposite direction, by increasing the after-tax return on capital. This happens
because, in the presence of congestion in utility services, a consumption tax
will increase the relative price of consumption and lower that of private capital;
see (12b). However, the impact of these tax rates on intertemporal welfare will
depend crucially on the private allocation of resources between consumption
and private investment. This allocation in turn will depend on (i) the elasticity
of substitution in production and (ii) the relative importance of the public good
in the utility function. These insights give us an important basis for comparing
the dynamic effects of the two competing fiscal instruments, that is, the income
and consumption tax rates, which we will consider in section 5 by undertaking a
numerical analysis of the model.
4.2. Optimal fiscal policy
Given that income and consumption taxes impact the economy in very different
ways, what tax and expenditure rates in the decentralized economy will replicate
the social planner’s optimum? Let these choices be represented by the vector
= (ĝ, τ̂y , τ̂c ). Then, by definition, is a description of optimal fiscal policy in
the decentralized economy. To determine these optimal choices, we will compare
the equilibrium outcome in the decentralized and centrally planned economies.
Since our focus is on the two distortionary tax rates, we will assume that g is set
optimally at ĝ, given by the solution to (10), and is appropriately financed by
some combination of non-distortionary lump-sum taxes and government debt.
Given ĝ, a comparison of (10b) and (14b) yields the following long-run optimal
relationship between the income and consumption tax rates:13
τy =
A−ρ (1 − α)(1 − σy )(y/z)ρ + θ (1 − σc )(1 + τc )(c/y)
.
A−ρ [α + (1 − α)(1 − σy )z−ρ ]yρ
13 Again, without any loss of generality, we set δ K = δ g = 0.
(15)
1484
S. Chatterjee and S. Ghosh
From (15), we see that in the presence of congestion in both production and
utility, only one tax rate can be chosen independently to attain the first-best equilibrium.14 This implies that the government has a choice in the ‘mix’ between the
income and consumption tax rates: if one is set arbitrarily, the other automatically adjusts to satisfy (15) to replicate the first-best allocation. But what kind of
a policy ‘mix’ must the government choose? Given (15), a unique combination
of τ y and τ c is unattainable. However, even if one individual tax instrument is at
its non-optimal level, (15) suggests that the government can still adjust the other
appropriately to attain the social optimum.
To see this flexibility in designing optimal fiscal policy, note that, in (15), the
income and consumption tax rates are positively related. A useful benchmark,
then, is to derive the tax on income, say, τ̂y , when τ c = 0. Given this benchmark
rate, we can evaluate the role of the consumption-based tax when the actual
income tax rate, τ y , differs from its benchmark rate, τ̂y . When consumption taxes
are absent, that is, τ c = 0, the appropriate tax on income is given by
τ̂y =
A−ρ (1 − α)(1 − σy )(y/z)ρ + θ (1 − σc )(c/y)
> 0.
A−ρ [α + (1 − α)(1 − σy )z−ρ ]yρ
(15a)
Therefore, the income tax rate required to attain the first-best optimum must
correct for both sources of externalities, σ y and σ c , taking into account the impact
of the public good on utility, θ . Even if the production externality is absent, that
is, σ y = 1, but the consumption externality is present, that is, 0 < σ c < 1, the
optimal income tax must be positive, to correct the distortions in utility caused
by private investment. Also, note that when public capital provides direct utility
benefits (θ > 0), the optimal income tax rate is higher than those derived in the
previous literature, namely, Barro (1990), Futagami, Morita, and Shibata (1993),
and Turnovsky (1997).
Now suppose that the actual income tax rate is different from its benchmark
rate derived in (15a). The government has a choice to use the consumption tax to
correct for this deviation, yet attain the first-best optimum without altering the
income tax rate. To see this, subtract (15a) from (15):
τc =
A−ρ [α + (1 − α)(1 − σy )z−ρ ]yρ τy − τ̂y .
θ (1 − σc )(c/y)
(16)
Therefore, when τy > τ̂y , the government must introduce a positive consumption
tax (τ c > 0) to attain the first-best equilibrium. On the other hand, if τy < τ̂y , a
consumption subsidy (τ c < 0) is the appropriate corrective fiscal instrument. In
14 Note that (15) holds only at the steady state and should therefore be viewed as a long-run
relationship. In general, in models with multiple state variables (such as this), the transitional
paths of the decentralized and the centrally planned economy will differ, requiring time-varying
tax rates in the decentralized economy in order to replicate the social planner’s transition path.
Owing to space constraints, we refer the reader to expositions in Turnovsky (1997), Benhabib,
Qinglai, and Nishimura (2000), and Mino (2001).
Dual nature of public goods and congestion
1485
the case where τy = τ̂y , as in (16), the consumption tax must be zero (τ c = 0). The
intuition behind this result can be explained as follows. When the income tax rate
is above its benchmark rate given in (15a), the private return on capital falls below
its socially optimal return. In this case, a positive tax on consumption helps offset
this deviation by raising the private return to capital relative to consumption.
Conversely, if the income tax rate is below its benchmark rate, then the private
return on capital exceeds its social return and a consumption subsidy corrects
this deviation by lowering the private return on capital relative to consumption.
Of course, when there is no congestion in utility (σ c = 1) or when the public good
is purely a productive input (θ = 0), this margin of adjustment is non-existent
and the consumption tax has no bearing on the equilibrium allocation. In this
case, the optimal tax on income is the only corrective fiscal instrument and is
similar to that obtained in the public-capital growth literature:15
τ̂y =
(1 − α)(1 − σy )
.
[αzρ + (1 − α)(1 − σy )]
Our discussion of optimal fiscal policy can be evaluated by relating it to the corresponding literature on congestion, taxation, and growth. A useful benchmark
in this literature is a paper by Turnovsky (1996). In that paper, a consumption
tax is non-distortionary and works like a lump-sum tax, and it must be reduced
to zero as the degree of congestion increases, while the income tax emerges as the
sole policy instrument when there is proportional congestion. When there is no
congestion in production, the optimal income tax rate is zero and government
expenditure must be financed by the non-distortionary consumption tax. Our
results can be viewed as both a refinement and a generalization of these results.
First, we show that under certain very plausible conditions, the consumption tax
is distortionary, both in transition as well as in steady state. Second, we show
that a consumption-based fiscal instrument (in the form of a tax or subsidy) can
be used jointly with an income tax to correct for different sources of congestion
in an economy. Third, when there is no congestion in production (σ y = 1), the
income tax rate must still be positive, with or without a consumption tax or
subsidy, to correct for distortions in utility. Finally, when there is no congestion
in utility (σ c = 1), the consumption tax is non-distortionary and our results are
comparable to those in Turnovsky (1996) as well as most of the literature.
5. Fiscal policy and economic welfare: a numerical analysis
We begin our analysis of the framework laid out in sections 3 and 4 with a numerical characterization of both the centrally planned and decentralized equilibria.
In particular, we are interested in (i) analyzing the role played by the relative
15 For an example with the Cobb-Douglas specification, see Turnovsky (1997).
1486
S. Chatterjee and S. Ghosh
importance of the public good in utility (θ ) in the propagation of fiscal policy
shocks and (ii) the sensitivity of the welfare responses to various fiscal shocks
to (a) the elasticity of substitution in production, (b) the congestion parameters,
and (c) the relative importance of the public good in the utility function.
5.1. The first-best equilibrium
Our starting point is the steady-state equilibrium in the centrally planned economy. The following table describes the choices of the structural and policy parameters we use to calibrate this equilibrium:16
Preference parameters : γ = −1.5, β = 0.04, θ ∈ [0, 0.3]
Production parameters : A = 0.4, α = 0.8, s ∈ [0.5, ∞], δK = δg = 0.08
The preference parameters β and γ are chosen to yield an intertemporal
elasticity of substitution in consumption of 0.4, which is consistent with Guvenen
(2006). Since there is no known estimate of θ , the relative weight of the public
good in the utility function, we consider a range between 0 and 0.3, where θ = 0
corresponds to the standard public capital-growth framework, where the public
good is only a productive input and θ = 0.3 corresponds to the estimate of the
ratio of public consumption to private consumption used by Turnovsky (2004).17
The output elasticity of private capital is set at 0.8, which is reasonable if we
consider private capital to be an amalgam of physical and human capital, as in
Romer (1986). This of course implies that the corresponding output elasticity for
the public good is 0.2, which is consistent with the empirical evidence reviewed
by Gramlich (1994). Given the paucity of empirical evidence on the elasticity
of substitution between private capital and public goods in production (s), we
choose a range between 0.5, indicating low substitutability between K and Kg ,
and infinity, indicating perfect factor substitutability.18 The case where s = 1
(ρ = 0) represents the familiar Cobb-Douglas technology and will serve as a
useful benchmark. Finally, the depreciation rates on the two capital stocks are
set to equal 8% each, and this serves as a plausible benchmark.
Table 1 characterizes the first-best optimum for different values of θ . When θ =
0, the equilibrium outcome corresponds to the case where the public good is only a
16 The calibration of the model is purely for illustrative purposes, rather than approximating a real
economy. The introduction of adjustment cost functions for private and public investment
would enable the calibration of a real economy, as in Turnovsky (2004). However, the central
results of our analysis would remain qualitatively unaffected by these changes.
17 It should be noted here that Turnovsky (2004) treats the public good in the utility function as a
pure consumption good, with no productive effects, as does most of the literature, where public
consumption and investment goods are clearly distinguishable. Moreover, treatments of public
consumption goods typically consider a flow of services, whereas in our case it is the
accumulated stock that is relevant.
18 The only exception is Lynde and Richmond (1993), who estimate the elasticity of substitution
between public and private capital in the context of a more general translog production function
for the manufacturing sector in the U.K.
Dual nature of public goods and congestion
1487
TABLE 1
Benchmark equilibrium in the centrally planned economy The Cobb-Douglas case (s = 1)
θ =0
θ = 0.1
θ = 0.3
ẑ
ĉ
ĝ
Ĉ/Y
K̂/Y
ˆ (%)
0.25
0.308
0.419
0.143
0.146
0.151
0.106
0.127
0.163
0.468
0.462
0.449
3.299
3.170
2.976
4.90
5.01
5.05
TABLE 2
Optimal public investment in the centrally planned economy (ĝ = G/Y )
s = 0.5
s=1
s→∞
θ =0
θ = 0.1
θ = 0.3
0.181
0.106
0.001
0.192
0.127
0.040
0.204
0.163
0.099
productive input. Therefore, considering the outcomes when θ > 0 provides useful
insights into its role in resource allocation. For example, when θ = 0, the optimal
ratio of the public good to private capital (ẑ) is 0.25, while the corresponding value
for the consumption-capital ratio (ĉ) is about 0.14. Optimal public expenditure
(ĝ) is about 10.6% of aggregate output. The consumption-output and capitaloutput ratios are 0.47 and 3.3, respectively, while the steady state is characterized
by a balanced growth rate of 4.9%. As θ increases, the utility return from public
expenditure increases, thereby augmenting its total return, causing the central
planner to allocate a larger fraction of output to the public good relative to
private investment. This is reflected by an increase in the equilibrium levels of
ẑ and ĝ. A larger stock of the public good, being complementary to private
consumption, facilitates the consumption of the private good, leading to an
increase in ĉ. The consumption-output and capital-output ratios are lower for
higher values of θ , indicating that the higher ĝ expands output proportionately
more than consumption and private capital. As θ increases, the larger fraction of
output allocated to public spending increases the productivity of private capital,
leading to higher equilibrium growth relative to the case when θ = 0.
Table 2 illustrates the optimal rates of public expenditure for variations in
both θ and the elasticity of substitution, s. As in table 1, we see that for any
given s, an increase in θ will lead the planner to allocate a higher fraction of
output to investment in the public good. On the other hand, for any given θ ,
an increase in the elasticity of substitution lowers the optimal allocation of ĝ.
This happens because a larger s increases the return on private capital relative
to the public good, leading the planner to allocate fewer resources to the public
good and more to private capital on the margin. An interesting feature of table 2
is the relationship between the rate of optimal public expenditure, the relative
weight of the public good in utility, and its output elasticity. For example, in
1488
S. Chatterjee and S. Ghosh
the flow model of Barro (1990), the optimal rate of public investment is given
by, say, g∗ = 1 − α = 0.2 (since α = 0.8 in our calibration), that is, by setting
the rate of public investment equal to its output elasticity. Turnovsky (1997)
shows that when public investment is treated as a stock rather than a flow,
g∗ < 1 − α. In table 2, this corresponds to the case where θ = 0, and let us denote
this rate by ĝθ=0 . Our numerical results show that when the dual benefits of the
public good are internalized by the planner (θ > 0), the optimal rate of public
expenditure, say, ĝθ>0 , is still lower than (1 − α), but is higher than ĝθ=0 , that
is, ĝθ=0 < ĝθ>0 < g∗ = 1 − α. For example, when s = 1, and θ = 0, ĝθ=0 = 0.106.
But when θ = 0.3, ĝθ>0 = 0.163. Therefore, internalizing the dual nature of the
public good generates an optimal expenditure rate that is less than in Barro (1990)
but larger than in Turnovsky (1997).
5.2. Equilibrium in a decentralized economy
Table 3A characterizes the benchmark equilibrium and long-run effects of fiscal
policy shocks in a decentralized economy for the Cobb-Douglas production
function (s = 1) and for different values of θ . As a benchmark specification, we
consider the case of partial congestion, where σ y = σ c = 0.5.19 The pre-shock
value for g is set arbitrarily at 5% of GDP, and is financed entirely through a
non-distortionary lump-sum tax (equivalent to government debt), so that τ y =
τ c = 0. For example, with θ = 0, the ratio of the public good to private capital is
about 0.1, while the consumption-capital ratio is 0.12. The agent devotes about
46% of output to consumption, while the capital-output ratio is 3.94. Finally,
these allocations lead to a long-run balanced growth rate of about 4.34%.
5.2.1. Long-run effects of fiscal policy shocks
The panels of table 3B report the long-run impact of five fiscal policy shocks
on the equilibrium allocation in the decentralized economy for different values
of θ . The first three (labelled I–III) pertain to an increase in g from 5% to 8%
of GDP, financed by (I) an increase in lump-sum taxes, (II) an increase in the
income tax rate, τ y , and (III) an increase in the consumption tax rate, τ c . In each
case, the tax increase finances only the increment in government spending, the
pre-shock rate of spending being financed by lump-sum taxes. The last two policy
shocks relate to the replacement of the lump-sum tax as a means of financing the
benchmark rate of government spending by introducing (IV) an income tax and
(V) a consumption tax. In experiments IV and V, the lump-sum tax is reduced to
zero as it is replaced by an income or consumption tax to finance the benchmark
rate of government spending. In our discussion below, we will focus on two sets
of comparisons, between policy changes I–III and IV and V.20
19 Even though we set the two congestion parameters to be equal, we will consider the sensitivity
of the results to their variation in table 4B.
20 While our analysis here is focused on comparisons across steady states, we have also analyzed
the transitional dynamics for the policy shocks described above. In the interest of space, we will
make the results available only upon request.
V
0.066
0.007
−0.018
−0.371
0.951
7.013
0.004
0.006
0.019
−0.031
−0.387
0.239
0.066
0.007
−0.019
−0.370
0.962
9.039
0.069
0.011
−0.008
−0.387
0.714
9.522
II
0.065
0.007
−0.020
−0.368
0.999
8.956
III
0.004
0.006
0.019
−0.031
−0.378
0.226
IV
I
0.066
0.007
−0.020
−0.368
0.984
11.875
−0.0002
−0.0003
−0.001
0.002
0.021
−0.023
θ = 0.3
V
0.4639
0.4649
0.4664
C̃/Y
0.069
0.010
−0.009
−0.384
0.747
12.363
II
3.9401
3.9390
3.9360
K̃/Y
0.064
0.005
−0.025
−0.361
1.089
11.624
III
0.004
0.005
0.018
−0.029
−0.360
0.224
IV
Description of policy shocks:
I.
A lump-sum tax-financed increase in government spending, g = 0.05 to 0.08; dg = 0.03
II. An income tax-financed increase in government spending, dg = dτ y
III. A consumption tax-financed increase in government spending, dg = (c̃/ỹ)dτc + τc d(c̃/ỹ)
IV. The income tax replaces lump-sum tax/government debt to finance the benchmark rate of government spending, g = τ y
V. The consumption tax replaces lump-sum tax/government debt to finance the benchmark rate of government spending, g = (c̃/ỹ)τc
0.070
0.011
−0.007
−0.389
0.695
7.496
0
0
0
0
0
0
0.066
0.007
−0.018
−0.371
0.951
7.013
IV
d z̃
d c̃
d(C̃/Y )
d(K̃/Y )
d ψ̃
d W̃ (%)
III
I
II
I
Policy →
0.1177
0.1180
0.1185
c̃
θ = 0.1
0.1029
0.1031
0.1034
z̃
B. Long-run effects of fiscal policy shocks
θ =0
θ =0
θ = 0.1
θ = 0.3
A. Benchmark equilibrium
TABLE 3
Equilibrium in a decentralized economy with congestion
Structural parameters: A = 0.4, β = 0.04, γ = −1.5, α = 0.8, s = 1, δ K = δ g = 0.08, σ c = σ y = 0.5
Base (pre-shock) policy parameters: g = 0.05, τ y = 0, τ c = 0
−0.001
−0.001
−0.003
0.005
0.060
−0.065
V
4.337
4.317
4.286
ψ̃(%)
1490
S. Chatterjee and S. Ghosh
An increase in government spending. In general, an increase in government spending leads to a higher flow of investment in the public good, thereby increasing
its long-run stock relative to private capital. The larger stock of the public good
increases the long-run productivity of private capital, thereby encouraging an increase in private investment. As the flow of output increases because of the shift
towards (public and private) investment, private consumption also increases.
However, given the higher stocks of private capital and the public good, output increases more than in proportion to both consumption and private capital,
leading to declines in their respective proportions in total output. The investment
boom also increases the long-run equilibrium growth rate and welfare. The increase in welfare can be attributed to two factors: (a) an indirect effect, operating
through the investment channel which, by increasing the flow of output, generates a higher flow of consumption, and (b) a direct effect, since the increase in
the stock of the public good lowers relative congestion and leads to an increase
in the proportion of utility services derived from its stock.21
As the relative importance, θ , of the public good in the utility function increases (i.e., its ‘dual’ role is recognized), the growth effect of an increase in
government spending becomes smaller, while the welfare effect becomes larger.
This is because, when θ > 0, an increase in the stock of the public good raises the
marginal valuation of consumption (through the public good’s utility services),
which has a dampening effect on growth and a magnifying effect on welfare.
Comparing policies I–III in table 3B, we see that an increase in spending financed by increasing the income tax leads to the highest welfare gain among the
three financing policies. This can be attributed to two reinforcing factors: (a) the
greater substitution towards consumption due to the lower after-tax return on
capital, and (b) the smaller increase in the stock of private capital, which in turn
generates higher services from the public good in the utility function by reducing
congestion. This result is robust to variations in θ . The consumption tax is identical to a lump-sum tax when θ = 0, but for positive values of θ the consumption
tax is indeed distortionary and, interestingly, is the most distortionary of the three
financing policies. In fact, the consumption tax-financed increase in government
spending leads to the smallest improvements in long-run welfare when compared
with the cases of lump-sum and income tax-financing. This can be attributed to
(a) the relative fall in private consumption due to a decrease in its after-tax return
and (b) the increase in the after-tax return on private capital when θ > 0 (see
equation 12b), which worsens the distortions created by congestion from the use
of the public good in the utility function.
21 Changes in welfare levels are computed by an equivalent variation in output across
steady-states; that is, we determine the percentage change required in the initial output level,
Y (0) (and therefore in the output flow over the entire base path), such that the agent is
indifferent between the initial welfare level and the welfare following the policy change, as in
Turnovsky (2004). The details of this derivation are available upon request.
Dual nature of public goods and congestion
1491
Tax policies to finance the benchmark rate of government spending. In policy experiments IV and V in table 3B, the lump-sum tax is replaced by an income
tax or a consumption tax to finance the benchmark rate of government spending (5% of GDP), respectively. In each case, the lump-sum tax is reduced to
zero to maintain the government’s balanced budget. In effect, these represent
two types of tax policy changes for a given level of government spending. The
introduction of an income tax reduces the after-tax return to private capital
and leads to a decline in its stock. By reducing the stock of capital, the income
tax reduces congestion in the production function. As a result of this policy
shock, both z̃ and c̃ rise. The substitution away from capital (and towards consumption) leads to a decline in the long-run growth rate. However, this shift in
favour of consumption is good from a welfare perspective, as welfare increases
with an increase in θ . A policy implication is that the more the public good
generates utility services (i.e., the higher is θ ), the more effective is the income
tax as an instrument for reducing congestion from a given level of government
spending.
When θ = 0, the consumption tax is completely non-distortionary and does
not change the equilibrium resource allocation. However, as θ increases, the
effects of replacing the lump-sum tax with a consumption tax contrast sharply
with those from the introduction of an income tax. The higher consumption
tax, by raising the after-tax return on private capital, draws more resources
away from consumption, reducing the services derived from the public good
in the utility function. The consequent increase in private investment reduces
both z̃ and c̃ and increases the long-run growth rate. However, such a policy
is socially undesirable, a consumption tax makes the economy worse off by
drawing resources away from consumption into capital, which aggravates the
distortions from congestion. Therefore, in sharp contrast to the existing literature,
our experiments indicate that introducing a consumption tax to finance a given
level of government spending is actually more distortionary than an equivalent
increase in the income tax rate.
5.3. Welfare analysis
Our analysis in the previous section established the following key results related
to the welfare effects of fiscal policy changes:
(i) The welfare increases resulting from higher government spending rise with
θ , the relative importance of the underlying public good in utility,
(ii) The welfare increase from an increase in government spending is the highest
when it is financed by raising the income tax and the lowest when financed
by a consumption tax. This result is robust to changes in θ .
(iii) As a means of financing a given level of government spending, an increase
in the income tax has sharply contrasting welfare effects compared with
an equivalent increase in the consumption tax. While an income tax increase
1492
S. Chatterjee and S. Ghosh
improves welfare by mitigating congestion, a consumption tax increase worsens the distortions from congestion.
However, the above results were derived for the benchmark specification of
a Cobb-Douglas production function and a given level of (equal) relative congestion in the utility and production. It is instructive at this point to examine
whether these results are robust to variations in (i) the elasticity of substitution
in production and (ii) differential relative congestion in utility and production.
Tables 4A and 4B report the results of these sensitivity tests, respectively, for
changes in long-run welfare.
Table 4A reports the sensitivity of welfare changes to the various fiscal shocks
discussed above for different values of the elasticity of substitution in production,
s. In general, for any given θ , an increase in s lowers the welfare impact of an
increase in public spending. This happens because the larger s is, the higher is
the return from private investment relative to a given level of public investment.
Therefore, as s increases, higher public spending causes the agent to allocate
more resources to private investment by substituting away from consumption,
which has an adverse effect on welfare. Therefore, for higher values of elasticity
of substitution, an increase in government spending can be welfare reducing.
However, as θ increases, the negative effects of a larger s are more than offset
(or partially alleviated) as the higher dual benefits of public expenditure affect
both productivity and private consumption. Comparing the welfare changes
from policies I–III and IV and V in table 4A, we see that our previous results
remain robust to variations in the elasticity of substitution in production within
an empirically plausible range. In other words, an income tax-financed increase
in government spending yields the highest welfare gains, while the consumption
tax-financed increase yields the lowest gains.
Table 4B reports the welfare sensitivity to fiscal shocks for variations in the
relative congestion parameters, σ y and σ c . As before, our central results remain
robust to variations in these parameters: the income tax continues to yield the
highest welfare gains, while the consumption tax yields the lowest. When we
consider tax policy changes, the consumption tax worsens the distortions from
congestion, while the income tax alleviates these distortions. Note that when
σ c = 1, the public good does not congest the utility function and the consumption tax essentially behaves like a lump-sum tax. Therefore, only in the
case where there is no congestion in utility or production, that is, σ c = σ y =
1, the income tax is more distortionary than the lump-sum and consumption
taxes.
6. Conclusions
This paper analyzes the impact of fiscal policy in a growing economy, where
the accumulated stock of a composite public good generates dual services for
122.08
24.11
7.01
1.20
−2.92
−6.97
125.95
25.07
7.50
1.52
−2.71
−6.84
122.08
24.11
7.01
1.20
−2.92
−6.97
3.10
0.68
0.24
0.11
0.05
0.06
0
0
0
0
0
0
V
11.51
11.60
11.73
12.59
12.52
12.44
10.66
11.21
11.73
1.17
0.86
0.45
−0.35
−0.15
0
V
11.75
11.87
12.06
12.42
12.36
12.29
II
128.51
26.29
9.52
3.84
−0.18
−4.13
II
11.09
11.61
12.06
III
123.88
25.17
8.96
3.46
−0.42
−4.25
III
0.58
0.22
−0.26
IV
2.91
0.65
0.23
0.10
0.03
0.03
IV
−0.23
−0.07
0
V
−0.22
−0.05
−0.02
−0.02
−0.01
−0.01
V
11.99
12.16
12.44
I
σ y =1
126.53
26.68
11.88
6.89
3.35
−0.15
I
θ = 0.3
12.31
12.27
12.23
II
130.24
27.63
12.36
7.21
3.54
−0.09
II
11.56
12.06
12.44
III
124.35
26.20
11.62
6.71
3.23
−0.22
III
Description of policy shocks:
I.
A lump-sum tax-financed increase in government spending, g = 0.05 to 0.08; dg = 0.03
II. An income tax-financed increase in government spending, dg = dτ y
III. A consumption tax-financed increase in government spending, dg = (c̃/ỹ)dτc + τc d(c̃/ỹ)
IV. The income tax replaces lump-sum tax/government debt to finance the benchmark rate of government spending, g = τ y
V. The consumption tax replaces lump-sum tax/government debt to finance the benchmark rate of government spending, g = (c̃/ỹ)τc
σc = 0
σ c = 0.5
σc = 1
IV
I
III
I
II
σ y = 0.5
124.67
25.34
9.04
3.52
−0.38
−4.22
σy = 0
B. Welfare sensitivity to congestion parameters (σ y and σ c )
(s =1, θ = 0.3)
s = 0.5
s = 0.75
s =1
s = 1.25
s = 1.75
s→∞
IV
I
III
I
II
θ = 0.1
θ =0
A. Welfare sensitivity to the elasticity of substitution (s) and the relative importance of public capital in utility (θ )
(σ y = σ c = 0.5)
TABLE 4
Welfare sensitivity of fiscal policy shocks to structural parameters and congestion
0.06
0.05
−0.93
IV
2.59
0.61
0.22
0.10
0.03
0.02
IV
−0.08
−0.04
0
V
−0.56
−0.13
−0.07
−0.05
−0.04
−0.03
V
1494
S. Chatterjee and S. Ghosh
the private sector by simultaneously enhancing both productivity and welfare.
We motivate this idea by discussing examples of common public goods, such
as infrastructure, education, law and order, that can generate both productivity
and utility benefits for the private sector. This represents a departure from the
conventional modelling strategy in the public goods-growth literature, wherein
the role of such goods are generally compartmentalized to being either productivity or utility enhancing. Modelling for the differential effects of congestion
in the utility and productive services derived from such public goods, we show
that a consumption tax can be distortionary, with a transmission mechanism
that is qualitatively opposite to that of an income tax. This structure enables us
to generalize existing results in the literature on optimal fiscal policy by demonstrating the possibilities of using both income- and consumption-based tax or
subsidy policies as corrective instruments for congestion. The optimal fiscal policy rules we derive indicate greater flexibility in the choice of corrective policy
instruments relative to the sole reliance on the income tax that is prevalent in the
literature.
We also conduct several policy experiments to numerically examine the efficacy of different taxes as financing tools for government spending on public
goods. Our results indicate that financing an increase in government spending
through an increase in the income tax rate dominates lump-sum and consumption tax-financing policies when the services from the public good are congested.
In the presence of congestion, replacing the lump-sum tax with an income tax to
finance a given level of government spending improves welfare by reducing congestion. In contrast, the introduction of an equivalent consumption tax actually
worsens welfare by increasing the distortions from congestion. These results also
contrast sharply with the existing literature, where the consumption tax is often
viewed as the least distortionary source of financing government spending. Our
results therefore contribute to the fiscal policy-growth literature by highlighting
a new channel through which consumption taxes (or subsidies) might impact
an economy’s equilibrium and welfare, even in the absence of an endogenous
labour-leisure choice.
Given the recent policy shift in many developing countries towards market
provision of many public goods such as power generation, water and sewerage, irrigation, highway construction, communications, one fruitful extension of
this framework might be to analyze the role of consumption and income taxes
when a public good is privately provided. In that case, the consumption-based
financing policies might be an important determinant of the market price of
the public good by affecting the marginal rate of substitution between private
consumption and the privately provided public good. Another area of interest
might be to examine the implications of consumption taxation in models with an
endogenous labour-leisure choice, but in the presence of utility and productivity
enhancing public goods. Therefore, we hope that our results will provide the foundations for future research in the complex domain of public goods and economic
growth.
Dual nature of public goods and congestion
1495
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